Equivalent elastic moduli of a rock mass consisting of orthorhombic layers

Abstract

A stratified rock mass is considered to consist of a series of parallel layers each of which has orthorhombic elastic properties. When the thicknesses and properties of the layers vary with depth in either a random or systematic repeated fashion it is shown that the layered rock mass can be represented by an ‘equivalent’ homogeneous orthormbic elastic material. Expressions for the properties of this ‘equivalent’ material are given in terms of the elastic properties of the constituent layers. Examples results are plotted for a range of simple cases. Some of the values of the ‘equivalent’ properties are limited with respect to the extreme values of the properties of the layers. For example, it is most significant that for the ‘equivalent’ material the ratios of certain moduli are greater than the minima for the materials comprising the individual layers. These ratios relate moduli applicable to stress and strain parallelto the layering to moduli applicable to stress and strain parallel to the normal to the layering. The ‘equivalent’ material properties can be used in computations to predict stress distributions. Having obtained these stresses in the ‘equivalent’ material, equations are given that enable conversion to stresses in the individual layer materials. It is suggested that the orthorhombic layer theory developed can be adapted for other applications such as reinforced earth and jointed systems.